2005 AP CHEMISTRY FREE-RESPONSE QUESTIONS (Form B)

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1 2005 AP CHEMISTRY FREE-RESPONSE QUESTIONS (Form B) 6. Consider two containers of volume 1.0 L at 298 K, as shown above. One container holds 0.10 mol N 2 (g) and the other holds 0.10 mol H 2 (g). The average kinetic energy of the N 2 (g) molecules is J. Assume that the N 2 (g) and the H 2 (g) exhibit ideal behavior. (a) Is the pressure in the container holding the H 2 (g) less than, greater than, or equal to the pressure in the container holding the N 2 (g)? Justify your answer. (b) What is the average kinetic energy of the H 2 (g) molecules? (c) The molecules of which gas, N 2 or H 2, have the greater average speed? Justify your answer. (d) What change could be made that would decrease the average kinetic energy of the N 2 (g) molecules in the container? (e) If the volume of the container holding the H 2 (g) was decreased to 0.50 L at 298 K, what would be the change in each of the following variables? In each case, justify your answer. (i) The pressure within the container (ii) The average speed of the H 2 (g) molecules Copyright 2005 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents). 12 GO ON TO THE NEXT PAGE.

2 AP CHEMISTRY 2005 SCORING GUIDELINES (Form B) Question 6 Consider two containers of volume 1.0 L at 298 K, as shown above. One container holds 0.10 mol N 2 (g) and the other holds 0.10 mol H 2 (g). The average kinetic energy of the N 2 (g) molecules is J. Assume that the N 2 (g) and the H 2 (g) exhibit ideal behavior. (a) Is the pressure in the container holding the H 2 (g) less than, greater than, or equal to the pressure in the container holding the N 2 (g)? Justify your answer. The pressure in the container holding the H 2 (g) is equal to the pressure in the container holding the N 2 (g) because there is an equal number of moles of both gases at the same temperature and volume (P = nk, where the constant K = RT V ). correct choice. correct explanation. (b) What is the average kinetic energy of the H 2 (g) molecules? The average kinetic energy of the H 2 (g) molecules is J because both gases are at the same temperature. correct energy. (c) The molecules of which gas, N 2 or H 2, have the greater average speed? Justify your answer. H 2 (g) molecules will have the greater average speed. Both gases have the same average kinetic energy, but H 2 (g) has the smaller molar mass. Therefore, the H 2 (g) molecules will have a greater average speed because, at a given temperature, the average (root-mean-square) speed of gas molecules is inversely proportional to the square root of the molar mass of the gas: urms = ( 3RT ) 1 M correct answer with an explanation. Copyright 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents).

3 AP CHEMISTRY 2005 SCORING GUIDELINES (Form B) Question 6 (continued) (d) What change could be made that would decrease the average kinetic energy of the molecules in the container? The average kinetic energy of a gas particle depends on the temperature of the gas sample. To decrease the average kinetic energy of the gas particles in a gas sample, the temperature of the N 2 (g) would have to be lowered. correct answer with an explanation. (e) If the volume of the container holding the H 2 (g) was decreased to 0.50 L at 298 K, what would be the change in each of the following variables? In each case, justify your answer. (i) The pressure within the container The pressure would be doubled. PV is a constant when the temperature and number of moles of gas are held constant. Therefore, if the volume is halved the pressure is doubled. P 1 V 1 = P 2 V 2 If V 2 = 1 2 V 1, then P 1 V 1 = P V P 2 = 2 P 1 1 P 1 = P 2 ( 2 ) correct answer. correct explanation. (ii) The average speed of the H 2 (g) molecules The average speed is unchanged when the volume of the gas sample is halved. Average speed depends on changes in temperature, not changes in volume. correct answer with an explanation. Copyright 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents).

6 AP CHEMISTRY 2005 SCORING COMMENTARY (Form B) Question 6 Sample: 6A Score: 8 This response earned all 8 points: 2 points for part (a), 1 point for part (b), 1 point for part (c), 1 point for part (d), 2 points for part (e)(i), and 1 point for part (e)(ii). Sample: 6B Score: 6 The point was not earned in part (d) because changing the volume would not affect the kinetic energy: the v in the cited equation is velocity, not volume. Only 1 out of 2 points was earned in part (e)(i) because the response only indicates that the pressure increases, not that it doubles. Sample: 6C Score: 4 The point was not earned in part (b). The point was not earned in part (d) because changing the volume would not affect the kinetic energy. Only 1 out of 2 points was earned in part (e)(i) because the response only indicates that the pressure increases, not that it doubles. The point was not earned in part (e)(ii) because the speed does not change. Copyright 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for students and parents). 7

AP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 2. the

AP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 2 Let f be the function defined for x 0 with f ( 0) = 5 and f, the ( x 4) 2 first derivative of f, given by f ( x) = e sin ( x ). The graph of y